German Utility Specification No. 81 28 146 discloses an apparatus of the kind mentioned in which the double bags that have been severed from a tubular film along a transverse line by hot wire welding are deposited on stacking plates, which are carried by endless chains and are provided on opposite sides of their longitudinal center line with respective rows of stacking pins for receiving the bags. The means for separating the bag stacks comprise a heated knife, which can be moved up and down and severs the stacks in the severing station between the rows of stacking pins in an operation in which the stacking plate constitutes an abutment for the severing knife. Because the stacking plates constitute also the abutments for the heated knives, the plates must be relatively large and heavy in weight. For this reason the known apparatus constitutes a relatively expensive structure because the endless chains must be provided with stacking plates which must be adapted to constitute abutments for the cutting knife and which have the same spacing as the stacks to be transported by the chains.